Final Report Award Number G18AC00026 Site Response Models for the Atlantic and Gulf Coastal Plain

Martin C. Chapman and Zhen Guo

Department of Geosciences Virginia Polytechnic Institute and State University 4044 Derring Hall Blacksburg, Virginia, 24061 email: [email protected], telephone: (540) 231-5036

September 12, 2019

Report Period April 1 2018 – March 31, 2019

This material is based upon work supported by the U.S. Geological Survey under Grant no. G18AC00026. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the opinions or policies of the U.S. Geological Survey.

1

Abstract The Atlantic and Gulf Coastal Plain in the southern and southeastern United States contains extensive Cretaceous and Cenozoic sedimentary sequences of variable thickness. We investigated the difference in response of sites in the Coastal Plain relative to sites outside that region using Fourier spectral ratios from 17 regional earthquakes occurring in 2010-2018 recorded by the EARTHSCOPE transportable array and other stations. We used mean coda and Lg spectra for sites outside the Coastal Plain as a reference. We found that Coastal Plain sites experience amplification of low-frequency ground motions and attenuation at high-frequencies relative to average site conditions outside the Coastal Plain. The spectral ratios at high frequencies gave estimates of the difference between kappa at Coastal Plain sites and the reference condition. Differential kappa values determined from the coda are correlated with the thickness of the sediment section and agree with previous estimates determined from Lg-waves. Averaged estimates of kappa reach ~ 120 ms at Gulf coast stations overlying ~12 km of sediments. Relations between Lg spectral ratio amplitudes versus sediment thickness in successive frequency bins exhibit consistent patterns, which were modeled using piecewise linear functions at frequencies ranging from 0.1 to 2.8 Hz. For sediment thickness greater than ~ 0.5 km, the spectral amplitude ratio at frequencies higher than approximately ~3 Hz is controlled by the value of kappa. The peak frequency and maximum relative amplification at frequencies less than ~1.0 Hz depend on sediment thickness. At 0.1 Hz, the mean Fourier amplitude ratio (Coastal Plain/ reference) is about 2.7 for sediment of 12 km thickness. Analysis of residuals between observed and predicted ground motions suggests that incorporating the amplification and attenuation as functions of sediment thickness may improve ground motion prediction models for the Coastal Plain region.

2

Investigations Undertaken

We explored some of the differences in ground motion propagation for sites located within, versus outside, the Atlantic and Gulf Coastal Plain. Currently, ground motion prediction models are lacking for the Coastal Plain regions of the central and eastern United States. This study was a first step toward developing such a model. Figure 1 shows the study area and the seismic stations contributing data. Until recently, the relatively low levels of seismic activity and a lack of long-term operating seismic stations outside the New Madrid seismic zone have limited wave propagation studies in most parts of the Atlantic and Gulf Coastal Plain. Previous studies documented high-frequency attenuation in the Gulf Coastal Plain. Gupta et al. (1989) found lower Lg Q in the Gulf region than elsewhere in eastern North America. The operation of the Earthscope USArray Transportable Array (TA network) in the central United States during 2010-2012 when a series of moderate earthquakes occurred in Oklahoma, Arkansas and Texas resulted in an important data set. More recently, a few earthquakes have been recorded in the Atlantic Coastal Plain by the currently operational Central and Eastern United States Network (N4 network), the United States National Seismic Network (US network) and some other stations, including temporary array deployments. Pasyanos (2013), using Q tomography, found lower Q for crustal S waves in the Gulf coastal region than in regions to the north. Chapman and Conn (2016) observed geographic variation of the attenuation parameter kappa, 0, (Anderson and Hough, 1984) in the Gulf Coastal Plain, noting a clear positive correlation of 0 and the thickness of post-Jurassic sediments in the region. Incorporating a thickness-dependent Lg kappa model in stochastic ground motion simulations resulted in improved high-frequency ground motion prediction (Chapman and Conn, 2016). Figure 10 of Chapman and Conn (2016) shows that the area with largest kappa (and thickest Coastal Plain sediment) largely corresponds with the low Q Gulf Coastal Plain area resolved by Cramer (2018) using USArray (TA network) data. It also corresponds with the area that has experienced continental crustal thinning (Salvador, 1991a, Sawyer et al., 1991, Thomas, 2010). Lg propagation is known to be sensitive to changes in crustal structure (Kennett, 1986). Both Lg blockage due to crustal thinning, and absorption due to the increase in thickness of sediments may operate to increase attenuation in parts of the Gulf Coastal Plain. Chapman and Conn (2016) jointly estimated shear wave crustal Q associated with distance dependent attenuation and site terms for Lg wave Fourier amplitude spectra. They used the site 0.62 terms to estimate 0 in the Gulf Region. They found Q =365f , where f is frequency in Hz. Chapman and Conn concluded that the bulk of the attenuation in the Gulf Coastal Plain is not strongly related to crustal waveguide Q, but instead is dominated by near-receiver attenuation reflected by kappa values that are correlated with local sediment thickness. Recently, Cramer (2018) estimated Q = 259f0.72 for the Gulf coastal region. Relative to the results of Chapman and Conn (2016) and Cramer (2018), representative estimates of Q outside the Coastal Plain in eastern North America show higher values at 1 Hz by a factor of approximately 1.4 – 2.0, but significantly less frequency dependence. For example, Atkinson and Boore (2014) found Q= 525f0.45 for rock sites in eastern North America. These models predict lower Q in the Coastal Plain at frequencies less than approximately 8-14 Hz, but higher Q at higher frequencies. Purely on the basis of these crustal Q estimates, one might expect lower amplitudes in the Gulf at low frequencies, and similar or larger amplitudes at frequencies of approximately 12 Hz, relative to the average of sites outside the Coastal Plain. In this study we observed that Coastal Plain sites 3

Figure 1. Geologic map of the central and eastern United States. Locations and station codes of the Earthscope Transportable Array (TA) stations (triangles), the United States National Seismic Network (US) stations (hexagons), the Central and Eastern US Network (N4) stations (circles), the Lamont-Doherty Cooperative Seismographic Network (LD) stations (stars) and the Southeastern Suture of the Appalachian Margin Experiment (Z9) stations (diamonds) used in this study are indicated. The thick solid curve shows the boundary of the Atlantic and Gulf Coastal Plain. Adapted from Garrity and Soller (2009). exhibit smaller high frequency amplitudes and larger low-frequency amplitudes than average site conditions outside the Coastal Plain. The origin of the strong frequency dependence of the reported estimates of crustal Q(f) for the Gulf Coastal Plain may represent complex trade-offs between site terms, source terms and distance dependent attenuation parameters in the regression models used to invert for crustal Q. It is our view that ground motion prediction models for Coastal Plain sites will require information in addition to the estimated value of Q for the crustal waveguide. The higher frequency (greater than 1 or 2 Hz) attenuation as well as the amplitude and frequency range of low frequency amplification we observe in the Coastal Plain is geographically variable and is dependent on the thickness of sediments (Chapman and Conn, 2016). 4

The motivation for this study was simple. We attempted to quantify, in a straightforward way, the relative difference between site response in the Coastal Plain (Atlantic and Gulf) and the region outside the Coastal Plain in terms of the Fourier amplitude spectra. We focused on spectral ratios because we wanted to establish a basis for modifying existing or future ground motion prediction models established for rock-like conditions for application in the Coastal Plain. The existing ground motion prediction models are to a large degree founded on results derived from the stochastic method of ground motion simulation, and our approach here is amenable to the development of target spectra for stochastic simulation. We expanded the dataset used by Chapman and Conn (2016) by adding broadband stations in addition to the TA network and data from a few more recent earthquakes including some occurring in the Appalachian region. Selecting reference sites is an important step in the spectral ratio method (e.g., Borcherdt, 1970). Our study is handicapped by a lack of information on shallow geologic conditions and near-surface velocity at the great majority of recording locations. Most of the stations outside the Coastal Plain are not sited on hard rock outcrop, but instead have site conditions ranging from thin residual soil over hard crystalline rock (many sites in the Appalachian Piedmont), to sites on thick sequences of Paleozoic sedimentary rock (e.g., stations in the Appalachian Valley and Ridge, and many stations in the mid-continent area). We used mean coda and Lg spectra derived from large numbers of stations outside the Coastal Plain as the reference condition. This approach is simple, but it lacks rigor and introduces some ambiguity. Most of our data are from recent (post-2009) shocks occurring outside the Coastal Plain region. However, we find evidence that shocks occurring within the Coastal Plain produce motions outside the Coastal Plain that have reduced amplitudes at high frequency, an observation that suggests that Lg waves experience appreciable high-frequency attenuation near the source if in the Coastal Plain.

Data and Analysis Figure 2 shows the locations of the 17 earthquakes used in this study, with the hypocenter locations, dates, moment magnitudes and depths (derived by Robert Herrmann: see Data and Resources) of the earthquakes listed in Table 1. Twelve of these earthquakes were located in Oklahoma, Arkansas and Texas, with five occurring in the Appalachian region. The stations that provided seismic data include the USArray (TA) stations, United States National Seismic Network (US) stations, Central and Eastern US Network (N4) stations, the Lamont- Doherty Cooperative Seismographic Network (LD) stations and the Southeastern Suture of the Appalachian Margin Experiment (SESAME; Z9 network). The stations are plotted in Figure 1 with different symbols to distinguish the networks. Most of the TA stations were deployed in the study region during 2010-2012 and each operated for about 2 years. The Z9 network operated between 2010 and 2014 as three profiles extending from Georgia to northern Florida (Parker et al., 2013). The N4 network stations are a subset of the TA network and currently remain operational. Table 2 lists instrument type, sample rates and number of stations for the various networks. Broadband seismograms recorded within 1000 km of the earthquakes in Table 1 were downloaded from the Incorporated Research Institutions for Seismology (IRIS) Data Management Center (see Data and Resources). Each seismogram begins ~600 seconds prior to the earthquake origin time and lasts for 3600 seconds. We converted the recordings to ground

5

Figure 2. Epicenters of earthquakes (circles) used in this study. Sizes of the circles are scaled to the moment magnitude listed in Table 1. acceleration using the instrument transfer functions, applied a high-pass filter with corner frequency 0.01 Hz, and rotated the horizontal components to radial and transverse directions. Further data processing involved computing the Fourier amplitude spectra of coda and Lg waves, which required determination of coda and Lg time windows. Coda waves are scattered waves that have taken a variety of paths between source and receiver. The coda spectra are insensitive to the source radiation pattern, rupture complexities and hypocentral distance at sufficiently large lapse time (Frankel et al., 1990, Frankel, 2015, Wu and Chapman, 2016). For each individual earthquake, we defined the beginning of a common coda window at lapse time T0 +1.5Ts, where T0 is the origin time and Ts is the S-wave travel time to the most distant station chosen for analysis. The choice of the largest hypocentral distance used for analysis was a compromise between the size of the dataset and the signal-to-noise levels of the distant recordings. The entire coda window length was chosen to be 20 s for all earthquakes. The Lg arrival time as a function of hypocentral distance r (km) is r T = T + . (1) Lg 0 3.53 This model was developed by Chapman and Conn (2016) using data from the 28 February 2011 Arkansas earthquake, which is also included in our dataset. The following equation was used to define the duration of the Lg window td, T +t T +800 ∫ Lg d 푎2dt = 0.7 ∫ Lg 푎2dt, (2) TLg TLg where 푎 is the ground acceleration. The window contains the maximum amplitudes of the Lg waves. We applied a cosine taper to the initial and final 15% of the time windows and computed the Fourier amplitude spectra of coda and Lg waves using the horizontal-components. Noise 6

spectra were computed simultaneously using tapered windows starting at the beginning of the seismograms with the same durations as the corresponding coda and Lg windows. Then the geometric mean of the two horizontal-component spectra was calculated for subsequent analysis. We carefully selected seismograms with good signal-to-noise ratios over relatively wide frequency bands by visual inspection. Traces with strong modulations in the spectra were discarded. Only Fourier spectral amplitudes within frequency bands where the signal-to-noise ratio is larger than five were used for analysis, to minimize the effects of noise. Table 3 lists the total number of recordings, number of recordings in the Coastal Plain, as well as the distance range for each earthquake in the final dataset. Most of the sediment thickness values beneath stations in the Gulf Coastal Plain are adapted from Chapman and Conn (2016), which were determined from Salvadore, (1991b). Sediment thickness at stations further to the east in the Appalachian region were estimated from depth-to-basement contour maps by Herrick and Vorhis, (1963), Wait and Davis, (1986), Salvadore, (1991b), Lawrence and Hoffman, (1993) and Powars et al., (2015). Some examples of the data are shown in Figure 3 which shows radial and transverse acceleration seismograms from the 06 November 2011 Prague, Oklahoma earthquake, recorded at station N35A and station 440A at similar distances of ~590 km. Station N35A is in eastern Nebraska and is underlain by residual soils and weathered Paleozoic sedimentary rocks, while station 440A in the Gulf Coastal Plain is located on ~ 8 km of Mesozoic and Cenozoic sediments. The acceleration amplitudes at station 440A are smaller compared to station N35A. Comparison of the corresponding coda and Lg Fourier spectra in Figure 3 shows that ground motions recorded at Coastal Plain station 440A are larger at low frequencies (<0.6 Hz) and smaller at high frequencies (> 1 Hz) relative to station N35A. Acceleration recordings and Fourier amplitude spectra at Coastal Plain stations from the 15 Feb 2014 South Carolina earthquake and the 13 Oct 2010 Oklahoma earthquake exhibit similar behavior relative to sites outside the Coastal Plain (Figure 3).

Coda Analysis According to the single-scattering model for coda waves proposed by Aki and Chouet c (1975), the spectral amplitude Yij(f, t) of coda waves recorded at the jth station in the Coastal Plain at some lapse time t after the origin time of the ith earthquake can be expressed as c c Yij(f, t) = Si(f)Gj (f)E(f, t) , (3) c where Si(f) is the source spectrum and Gj (f) represents the site response for coda waves at the jth station, j=1,2,3..n. E(f, t) combines the coda scattering intensity and subsequent decay of the coda as a function of frequency and lapse time, which is assumed independent of source and station when the lapse time t is larger than ~1.5-2 times the S wave arrival time (e.g. Frankel, 2015, Wu and Chapman, 2017). Our major assumption is that E(f,t) is a property of the crust, shared by all earthquakes and stations, both within and outside of the Coastal Plain. This requires that the crustal waveguide be at least approximately the same for the region encompassing all the earthquakes and stations. As noted in the Introduction Section, previous studies of crustal Q have reported regional differences in the central and eastern United States, most significantly between the Gulf Coastal Plain on the one hand, and the Cratonic Platform - Appalachian region (outside the Atlantic Coastal Plain) on the other. Our hypothesis here (that we test using residual analysis) is that the lower Q values reported for the Gulf Coastal region at frequencies below approximately 10 Hz are due, at least in part, to trade-offs in the regression

7

models between distance dependent crustal attenuation (parameterized by a frequency-dependent quality factor Q) and strong geographically variable local attenuation, which can be

Figure 3. (a) Horizontal-component acceleration seismograms recorded at station 440A in eastern Texas and station N35A in eastern Nebraska, from the Mw 5.65 06 November 2011 earthquake in Oklahoma. The stations are at a distance of ∼ 590 km. The shaded areas from left to right denote the windows used for calculating Lg and coda spectra respectively. (b) Corresponding geometric mean of coda and Lg spectra from the two horizontal recordings at station 440A and station N35A using the windows defined in (a). (c) and (d) are the same as (a) and (b) but recorded at station W02 in northern Florida and station T56A in western Virginia, from the Mw 4.11 15 February 2014 earthquake in South Carolina, with epicentral distance of ∼ 390 km. (e) and (f) are the same as (a) and (b) but recorded at station 438A in southeastern Texas and station 433A in the Llano uplift of central Texas, from the Mw 4.33 13 October 2010 earthquake in Oklahoma, with epicentral distance of ∼ 500 km. 8

parameterized by , and is reflected in the site terms of the regression models. We recognize that differences in crustal structure (e.g., crustal thickness) exist throughout the central and eastern United States. We assume that differences between the response of stations at a fixed lapse time for a given earthquake are due to path differences arising near the receiver station c (i.e., site response), and involve Gj (f), in the case of stations in the Coastal Plain, as well as site response at stations outside the Coastal Plain. We distinguish the coda spectral amplitude at the kth station outside the Coastal Plain, at lapse time t for the ith earthquake, as ̂ 푐 ̂푐 푌푖푘(푓, 푡) = 푆푖(푓)퐺푘(푓)퐸(푓, 푡), (4) ̂푐 where 퐺푘(푓) represents the site response of a station outside the Coastal Plain. Our approach is to define a reference spectrum for each earthquake, based on the coda spectra at a fixed lapse time and recorded by stations outside the Coastal Plain. Site conditions outside the Coastal Plain, like conditions within it, are variable. Many non-Coastal Plain sites are on soil and alluvium, overlying weathered rock. The conditions may result in modulated amplification of the Fourier amplitude spectra at frequencies that depend on the thickness and ̂푐 velocity of the near-surface materials. These site response effects are contained in the 퐺푘(푓) term for the kth station. Visual inspection of all these spectra indicates that in most cases the modulations (if present) occur at frequencies greater than 1-3 Hz. Spectra exhibiting strong peaks were discarded. Stacking (averaging) the remaining spectra from different stations recording the same earthquake for a fixed lapse time reduces the amplitude of the modulations in the mean and the result is a “smooth” spectrum, given a sufficient number of individual spectra. Our reference spectrum for the ith earthquake is the mean of the coda spectra from the stations located outside the Coastal Plain, 푚 푚 1 S (f)E(f, t) 푌̅푐(푓, 푡) = ∑ S (f)퐺̂푐(f)E(f, t) = i ∑ 퐺̂푐(f), (5) 푖 푚 i 푘 m 푘 푘=1 푘=1 where m is the number of stations involved in calculating the mean reference spectrum. The coda spectral ratio for the jth station recording the ith earthquake is obtained by dividing equation (3) by the reference spectrum given by equation (5), c 푐 c Yij(f,t) 퐺푗 (푓) R (f) = = 1 . (6) j Y̅c(f,t) ∑푚 퐺̂푐(푓) i 푚 푘=1 푘 In equation (6), taking the ratio of the coda spectrum at the Coastal Plain station to the reference spectrum removes the source and path effects by cancellation. The result represents the response effects of the Coastal Plain site relative to the reference condition. The reference condition is the mean site response of all stations outside the Coastal Plain recording the ith earthquake. At high frequencies, the site response term for the jth Coastal Plain recording, which represents the numerator term in equation (6), exhibits exponential decay with frequency that we model as c Gj (f) = Ajexp(−πkjf), (7) where 퐴푗 is a constant. Here, kj (kappa) is analogous to k0 of Anderson and Hough (1984). It is a site-specific parameter that accounts for the near-receiver attenuation effects and describes the spectral decay at high frequencies (e.g., Anderson and Hough 1984, Atkinson and Boore, 2014). Likewise, we model the denominator term in equation (6) (the reference spectrum) at high frequencies as 9

푚 1 ∑ 퐺̂푐(f) = 퐴̅ exp(−π푘̅ f), (8) m 푘 r r 푘=1 ̅ where 푘r represents the “average” kappa for the reference condition. Substituting equations (7) and (8) into equation (6) leads to the following model for the logarithm of the coda spectral ratio at high frequencies c Aj ̅ ln(Rj ) = ln ( ) − π(kj − 푘r)f = Cj − π(훿푘푗)f, (9) 퐴̅r ̅ where Cj is a constant and 훿푘푗 = (kj − kr) is the difference between the kappa value (kj) at the ̅ jth Coastal Plain station and the average kappa ( kr ) at the reference sites. A linear regression of the natural logarithms of the coda spectral ratio in the frequency range between approximately 3 Hz and the high frequency signal limit imposed by noise provides an estimate of C j as the zero- frequency intercept and −π(훿푘푗) as the slope value. The measured slopes of equation (9) depend on sediment thickness at the station, whereas the intercept values are generally close to zero (e.g., Figure 4). The mean intercept (from 266 measurements) is 0.266 with a standard deviation of 0.412. Figure 4 shows some examples of the coda spectra and spectral ratios recorded at Coastal Plain stations on different thicknesses of sediment. In Figure 4 (a), we show the coda acceleration spectra recorded at Coastal Plain stations 440A and Z41A, as well as the reference spectrum from the 06 November 2011 Prague, Oklahoma earthquake. Sediment thickness is ~8.0 km at 440A and ~2.5km at Z41A. Relative to the mean reference spectrum, both Coastal Plain spectra are amplified at low frequencies (<1Hz) and attenuated at high frequencies. The corresponding natural logarithms of the coda spectral ratios (logarithm of equation 6), are also shown in Figure 4 (b). We note the high frequency (greater than ~ 2-3 Hz) spectral trends at station 440A show a steeper slope than at Z41A. The estimated difference in kappa, relative to the reference condition, from linear regression fits according to equation (9), is 161 ms and 62 ms for 440A and Z41A, respectively. The frequency range over which equation (9) holds depends on the degree and bandwidth of low-frequency amplification, and the signal-to-noise ratios at high frequency. For the example shown in Figure 4, this range, where the log spectral ratio versus frequency plot is linear, is from 2.5-11 Hz for 440A, and from 1-7 Hz for Z41A. This was determined from visual inspection of the coda spectra and the spectra of pre-signal noise. Also shown in Figure 4 are two additional examples involving different stations and earthquakes.

10

Figure 4. In the top panel, (a) shows the geometric mean of Fourier acceleration amplitude spectra for horizontal-component coda waves, computed from a 20 s window at a lapse time of 334 s after the origin time of the 06 November 2011 Prague earthquake in Oklahoma. The black line and gray line are computed from coda waves recorded at Coastal Plain stations 440A and Z41A, underlain by sediments of thickness ∼8 km and ∼2.5 km respectively. The thicker line is the mean coda reference spectrum computed for non-Coastal Plain stations. (b) Ratios of coda spectra at station 440A (black) and station Z41A (gray) shown in (a), to the mean reference spectrum (thicker line in (a)). The solid line segments indicate the frequency ranges of spectral ratios used for linear regression (thicker lines). (c) and (d) are the same as (a) and (b) but for coda waves from the 15 February 2014 South Carolina earthquake recorded at station W02 with sediment thickness ∼2.5 km and station W21 with ∼0.5 km of sediment. Coda spectra are calculated at a lapse time of 280 s after the event origin time. (e) and (f) are the same as (a), (b) but for coda waves from the 13 October 2010 Oklahoma earthquake recorded at station 438A with sediment thickness ∼8.0 km and station Z38A with ∼3.0 km of sediment. Coda spectra are calculated at a lapse time of 225 s after the event origin time.

11

Kappa model Figure 5 shows the  values determined in this study from the coda spectral ratios and the Lg kappa values determined by Chapman and Conn (2016) at Coastal Plain stations plotted versus the sediment thickness. The estimates of  values from coda spectral ratios agree well with the Lg kappa estimates, and both sets of values show correlation with the thickness of Coastal Plain sediments. The Lg kappa measurements by Chapman and Conn (2016) are from sites in the Gulf Coastal Plain with only 12 measurements on sediments less than 1 km thick. In contrast, 69  values were derived from stations on less than 1 km of sediment, and approximately 30% of those were from stations in the Atlantic Coastal Plain (east of 85º W longitude). The agreement between and Lg kappa implies that kappa for the reference condition is small, essentially negligible in comparison to kappa at the Coastal Plain stations examined here. The  values are the difference between kappa at the Coastal Plain sites and the reference model (equation 9). The thinnest sediment site in the Coastal Plain used to estimate  in this study has sediments 90 meters thick. Under our assumptions,  should be near zero for zero sediment thickness. In order to match this constraint, we use a log  versus log thickness regression model to fit the data. This type of model is supported by some simple theoretical 1-D wave propagation models we examined (Figure 6). We calculated theoretical kappa values from models for Coastal Plain sites with different sediment thickness, assuming a plane-layered velocity structure and vertical S-wave incidence. We approximated a gradient model for shear wave velocity and Q by using a large number of horizontal layers. Figure 6 shows an example shear wave velocity and Q model for sites with sediment thickness of 5 km and 12 km respectively. The model is crude, constrained by the compressional wave velocity profile near the Gulf coast by Van Avendonk et al. (2015), with very little information about S-wave Q as a function of depth in the Coastal Plain (Chapman et al., 2008). We assume that velocity and Q increase rapidly at shallow depth (less than 0.5 km), and that the increase with depth becomes more gradual at greater depths (Figure 6). The theoretical kappa values reflect this gradient behavior, increasing rapidly from zero at zero sediment thickness, and transitioning to a more linear increase for thickness greater than 0.5 km (Figure 6). Note that the purpose of the modeling shown in Figure 6 was simply to identify the form of the regression model to use for fitting the actual observations, shown in Figure 5. The final  model was derived by combining the measures from the coda and Lg kappa values (Chapman and Conn, 2016) as a function of sediment thickness Z. This was done because there appears to be no significant systematic difference in the two sets of measures, given the scatter in the observations. The result is ln(훿푘) = (−2.932 ± 0.029) + (0.339 ± 0.020) ln(푍), (10) or 훿푘 = 0.0533 푍0.339, (11) where  is in seconds and 푍 is in kilometers. The model above (equation 11) is plotted as a thick line in Figure 5. The dashed lines are the 84 percentile and 16 percentile levels, calculated by adding and subtracting the regression standard error estimate to the log-log data fit (Equation 10). The derivative of equation (11) is a decreasing function of Z, predicting a large change of  values with changes of thickness on thin sediment sections, which becomes less dramatic for thick sequences. This is consistent with our modeling (Figure 6) and may be due to the effects of sediment compaction under increasing

12

Figure 5. Differential kappa (훿푘) from linear least square regression of coda spectral ratios in this study (dots) and Lg kappa from Chapman and Conn (2016) (crosses) versus thickness of the post-Jurassic marine sedimentary section. Outliers at the 5% and 95% level from an initial regression were removed for the final regression results shown here. Solid line shows the least- square regression fit to both data sets, 훿푘 = 푒−2.932푍0.339 (regression model: 푙푛(훿푘) = (−2.932 ± 0.029) + (0.339 ± 0.020)푙푛 (푍)), where 푍 is the thickness of Coastal Plain marine sediment in km. The dashed lines are the 84 percentile and 16 percentile levels, calculated by adding and subtracting the regression standard error of estimate to the log-log data fit.

Figure 6. (a) Shear wave velocity and Q versus depth assumed for the Coastal Plain (5 km sediment thickness). (b) Same as (a) for 12 km sediment thickness. (c) Differential kappa (훿푘) values for the assumed model (dots), compared to observed and Lg kappa values (crosses).

13

confining pressure with depth. The model predicts a  value of ~ 0.053 s at 1 km thickness and a value of ~ 0.124 s for sediment thickness of 12 km.

Lg Analysis At low frequencies, the coda spectral ratios contain surface wave energy and may not be a good estimate of the relative site response for the higher amplitude parts of the seismogram that are associated with the Lg phase. Therefore, we calculated the spectral ratios of Lg waves which arrive earlier in the seismograms. We modeled the Lg spectral amplitude recorded at the jth Coastal Plain station from the ith earthquake as −πr f YLg(f) = S (f)GLg(f)P(r ) exp ( ij ), (12) ij i j ij Q(f)v where rij is hypocentral distance and P(rij) is the geometrical spreading term independent of Lg frequency and Gj (f) is Lg wave site response at Coastal Plain station j. Q(f) is the average quality factor for the crustal wave guide, which is assumed common to all stations and sources, and v is the average velocity of the Lg waves along the propagation path in the crust. We define the reference condition for the Lg phase in a manner similar to the approach used for the coda, by using a mean of Lg spectra from stations outside the Coastal Plain. However, the Lg spectra depends on the station distance r, and different stations experience different degrees of geometrical spreading and anelastic absorption. This is in contrast to the situation with the coda, where all the spectra are measured at the same lapse time. For the jth station in the Coastal Plain, we compute a corresponding mean reference spectrum using stations outside the Coastal Plain at distances that differ only slightly from rij, given by 푆 (푓) −πr f 푌̅퐿푔(푓) = 푖 ∑푚 퐺̂퐿푔(푓)P(r ) exp ( iq ) , (13) 푖푗 푚 푞=1 푞 iq Q(f)v for 0.95 rij ≤ riq ≤ 1.05rij and q = 1,2,3..m, where m is the total number of non-Coastal Plain ̂퐿푔 stations satisfying the ± 5% distance requirement and 퐺푞 (푓) is the site response for Lg waves at non-Coastal Plain station q. The Lg spectral ratio for the jth Coastal Plain station recording the ith earthquake is obtained by dividing equation (12) by the reference spectrum given by equation (13), −πr f Lg Lg ij Lg ( ) Gj (f)P(rij) exp ( ) ( ) Lg Yij f Q(f)v Gj f Rj (f) = Lg = ≈ . (14) Y̅ (f) 1 푚 퐿푔 −πriqf 1 푚 퐿푔 ij ∑ 퐺̂ (푓)P(r ) exp ( ) ∑ 퐺̂ (푓) m 푞=1 푞 iq Q(f)v m 푞=1 푞 Equation 14 assumes that the source radiation pattern is constant, for all stations. The Lg wave is comprised of multipath S waves that leave the source over a range of take-off angles, which tend to average out the radiation pattern at the higher frequencies. However this does not occur to the same degree as with the coda. We expect increased scatter in the Lg ratios due to radiation pattern effects.

Quantifying Site Response as a Function of Sediment Thickness As shown by example in Figure 4, the response of the Coastal Plain stations relative to the reference condition involves amplification at lower frequencies (less than 1-3 Hz) and attenuation at higher frequencies. These frequency-dependent effects appear to depend on the thickness of Coastal Plain sediments. Figure 5 shows that kappa (and the magnitude of

14

attenuation) is correlated with sediment thickness. It turns out that the degree of amplification and the frequencies at which the amplification occurs also depends on sediment thickness. We examined the behaviors of Lg spectral amplitude ratios with respect to sediment thickness at different frequencies. We combined spectral ratio measurements from all earthquake-Coastal Plain station pairs (equation 14). We assume that source radiation pattern effects are negligible, and that the observed spectral ratio of equation (14) is a good approximation of the ratio of the site response at a given Coastal Plain station relative to the reference condition. At a given station, for a given earthquake, we binned the spectral ratios according to frequency, using 12 successive frequency intervals (bins), 0.06-0.14, 0.14-46, 0.46- 0.66, 0.66-0.86, 0.86-1.26, 1.26-1.66, 1.66-2.46, 2.46-3.26, 3.26-4.86, 4.86-6.46, 6.46-8.06, 8.06- 11.26 Hz. The center frequencies of the intervals are 0.1, 0.3, 0.56, 0.76, 1.06, 1.46, 2.06, 2.86, 4.06, 5.66, 7.06 and 9.66 Hz, respectively. The binned value is the geometric mean of the spectral amplitudes in each frequency interval. Figure 7 plots the natural logarithms of the frequency-binned Lg spectral ratios as a function of sediment thickness at the recording station, for bin center frequencies ranging from 0.1 to 2.86 Hz. The scatter is large, but some trends can be discerned. At the lowest frequencies (0.1 and 0.3 Hz), the values are mostly positive and exhibit an increasing trend throughout the range of sediment thickness. At frequencies 0.56-0.76 Hz, the natural logarithms show overall positive values but exhibit a very slight linearly decreasing trend for thickness larger than ~1 km. As frequency increases (> 1.06 Hz), the logarithms of the Lg spectral ratios become negative at large thickness (> 3 km) with a linearly decreasing trend, indicating that attenuation effects of the sediments dominate at high frequencies and become stronger as thickness increases. The behaviors of the Lg spectral ratios are more complicated in the thickness range 0-3 km, as shown in the lower panels with a zoomed-in view in Figure 7. For insight as to how the relation between the Lg spectral ratios and the sediment thickness might behave, we simulated theoretical transfer functions for sites on sediments of different thickness ranging from 100 m to 12 km. We used 1-D plane-layered velocity and Q models (Figure 6) assuming vertical S-wave incidence and the quarter-wavelength approximation (Joyner et al., 1981, Boore and Joyner, 1991). We calculated theoretical spectral ratios by dividing the transfer functions for sediments by the transfer function of a model reference site (thin soil layer over basement rock). We found that the natural logarithms of the theoretical spectral ratios can be roughly approximated by bi- linear functions of sediment thickness with different transition thicknesses in a frequency range of 0.1-2.86 Hz. For a given frequency, these piecewise linear functions show a zero value of the natural logarithms of the spectral ratios at zero thickness and can be described as ln(푅) = 푎1 + 푏1푍, 0 ≤ 푍 ≤ 푍0, (15) ln(푅) = 푎2 + 푏2푍, 푍 ≥ 푍0, (16) where 푅 is the spectral amplitude ratio, 푍 is the sediment thickness in km and 푍0 is the transition thickness from one linear segment to the other. The coefficients 푎1, 푏1, 푎2 and 푏2 are constrained by the following conditions: 푎1 = 0, (17) 푎1 + 푏1푍0 = 푎2 + 푏2푍0. (18) The observed Lg spectra amplitude ratios in Figure 7 are modeled using equations (15) and (16) with constraints according to equations (17) and (18) using linear regression with the transition thickness Z0 at each frequency determined from the theoretical modeling. Figure 7 plots the resulting functions, representing site response effects of sediments in the frequency range of 0.1-2.86 Hz, with the transition thickness indicated by triangles. Table 4 lists the

15

parameters in equations (15 through 18) for different frequencies. The corresponding 84 percentile and 16 percentile levels were calculated by adding and subtracting the regression

Figure 7. Natural logarithms of Lg spectra amplitude ratios versus sediment thickness, averaged over 8 frequency bands. The thick solid lines indicate the piecewise linear regression model fit to the data. The corresponding 84 percentile and 16 percentile levels were calculated by adding and subtracting the regression standard error of estimate to the means, and are indicated by the dashed lines. The lower figure is zoomed into a smaller thickness range for a better view of the transition thickness (triangle).

16

standard error of estimate to the means, and are indicated by the dashed lines in Figure 7. The regression parameters for different frequencies are listed in Tables 5 and 6 respectively. Figure 8 plots the logarithms of the Lg spectral ratios at some specific frequencies from 4.06 to 9.66 Hz, versus recording site sediment thickness. The logarithms of the spectral ratios at these higher frequencies become increasingly negative (as frequency increases), indicating a transition from low frequency amplification to high-frequency attenuation which is most obvious for sites with thicker sediments. At frequencies higher than 2.86 Hz, (Figure 8), attenuation effects of the sediments dominate the site response. We modeled the general trends of the spectral ratios at high frequency successfully (Figure 8) using equation (9) and the sediment thickness-dependent  model given by equation (11). Figure 8 shows the predicted values of the Lg spectral ratio. The values were computed using the mean value of 0.266 determined from 266 measurements of the zero-frequency intercept term Cj in equation (9). Lg spectral ratio data at frequencies greater than 9.66 Hz are sparse, and show increasing scatter with frequency, largely due to lower signal/noise ratios at the higher frequencies. This is particularly the case for stations on thick sediment in the Gulf Coastal Plain. We estimated the Lg spectral ratio versus sediment thickness function at frequencies greater than 2.86Hz using equation (9) and the thickness-dependent  model (equation 11).

Figure 8. Natural logarithms of Lg spectra amplitude ratios (crosses) averaged in 4 successive frequency bins versus sediment thickness, compared to predicted amplitude ratios (dots) based on equation (9) with the model in equation (11). The shaded area shows the 84 percentile and 16 percentile range of the predicted amplitude ratios, based on the 16 – 84 percentile range of the model calculated by adding and subtracting the regression standard error of estimate to the log-log data fit (Equation 10).

17

Target Spectra for the Stochastic Method and Evaluation of the Site Response Model Using Residual Analysis We used the stochastic method of ground motion simulation to examine the potential use of our spectral ratio model for ground motion prediction in the Coastal Plain. The approach we used follows Chapman and Conn (2016). It involves calculation of a simulated Fourier amplitude spectrum (or “target” spectrum in the context of the stochastic method) using the spectral ratios defined in the previous sections. The residuals are the difference between the logarithms of the observed spectral amplitudes and the simulated target amplitudes. The stochastic ground-motion simulation method has been frequently used to model high frequency ground motion (e.g., Hanks and McGuire, 1981, Boore, 1983, Atkinson and Boore, 2006). The target Fourier amplitude spectrum used in the stochastic method, 푇(푓), is often represented as 푇(푓) = 푆표푢푟푐푒(푓)푃푎푡ℎ(푓)푆𝑖푡푒(푓), (19) where 푆표푢푟푐푒(푓) is the earthquake source spectrum, 푃푎푡ℎ(푓) represents the path effect of S- wave or Lg-wave propagation through the crust, and 푆𝑖푡푒(푓) is the site response effect in the vicinity of the recording site. The source spectra were modeled according to Brune (1970, 1971) as 2 푀0(2휋푓) 1 푆표푢푟푐푒(푓) = 퐵 푓 ( ), (20) 1+( )2 4휋휌훽3 푓푐 where 푀0 is the earthquake seismic moment, 푓푐 is the corner frequency, 훽 (assumed to be 3.53×105 cm/s) is the shear wave velocity at the source, and 𝜌 (assumed to be 2.7 푔/푐푚3) is the density at the source. The corner frequency 푓푐 is given by Δ휎 1 푓푐 = 0.491훽( )3 , (21) 푀0 2 where Δ𝜎 is the earthquake stress drop in units of dyn/cm , M0 is in units of dyn-cm and the shear wave velocity is expressed in units of cm/s. The constant 퐵 = 푅휃휙퐹푠푉, where 푅휃휙 is the radiation pattern (assumed to be 0.55), 퐹푠 is the free-surface effect for Lg (assumed here to be a factor of 2) and 푉 represents the effect of partition of motion onto two horizontal-components (0.71). The path term for Lg propagation can be expressed as −휋푓푟 푃푎푡ℎ(푓) = 푃(푟) exp ( ). (22) 푄(푓)푣 P(r) in equation (22) represents geometrical spreading. At distances beyond approximately 120 km, the Lg-phase exhibits surface wave (cylindrical) geometrical spreading (Wang and Herrmann, 1980, Herrmann and Kijko, 1983, Kennett, 1986). Near the source, where the S- wave field is dominated by direct arrivals, approximate body wave (spherical) spreading is expected, although both theoretical calculations for layered Earth models and empirical observations indicate that geometrical attenuation may differ somewhat from the theoretical 1/r far-field spreading for an isotropic source in a homogenous Earth. The apparent spreading may involve source radiation pattern, directivity, focal depth, and different behavior for the vertical and horizontal components (Ou and Herrmann, 1990, Chapman and Godbee, 2012, Atkinson and Boore, 2014, Frankel, 2015). In the distance range from approximately 60 to 120 km, post- critical reflections from the lower crust and the Moho are important, and the S-Lg wave packet amplitude tends to be approximately constant (Burger et al., 1987, Atkinson and Mereu, 1992, Atkinson, 2004). Chapman and Conn (2016) examined two geometrical spreading models in the

18

Gulf Coastal Plain. The models differ only in the nature of spreading at hypocenter distances less than 60 km. We tested both models with our expanded data set for this study. We settled on the following model as being most consistent with the data from all stations (both inside and outside the Coastal Plain region):

푃(푟) = 푟−1.0, 푟 ≤ 60 푘푚, (23) 푃(푟) = 60−1.0, 60 ≤ 푟 ≤ 120 푘푚, (24) 푟 −0.5 푃(푟) = 60−1.0 ( ) , 푟 ≥ 120 푘푚. (25) 120 The quality factor 푄(푓) for the crustal waveguide is assumed to be 푄(푓) = 600푓0.42. (26) The quality factor model was arrived at from analysis of residuals using many trials with different models. We looked at high Q models for paths in the Appalachians and central platform and low Q models in the Gulf region. The final model is similar to that of Atkinson and Boore (2014), for rock sites in northeastern North America. 푆𝑖푡푒(푓) in equation (19) is the site response term, dependent on the velocity structure and attenuation properties of materials beneath the recording site. As demonstrated in the previous sections, 푆𝑖푡푒(푓) for sites in the Coastal Plain differ substantially from the mean condition of sites outside the Coastal Plain. Here we assume the following model for the reference condition (average condition outside the Coastal Plain): 푆𝑖푡푒푟푒푓(푓) = 퐹exp(−πk0푓). (27) The amplification factor F is the crustal amplification factor of Boore and Thompson (2015) for stable continental regions and Vs30 = 2.0 km/s. Following Boore and Thompson, we adopted 푘0 = 0.006 s recommended by Hashash et al. (2014) for reference sites in Central and Eastern North America. For sites in the Coastal Plain, the site response term is 푆𝑖푡푒푐푝(푓) = 푆𝑖푡푒푟푒푓(푓)푅푎푡𝑖표(푓, 푍). (28) For frequencies in the range f = 0.1 - 2.86 Hz, Ratio(f,Z) = R, where R is given by equations (15) and (16) with parameters listed in Table 4. For frequencies greater than 2.86 Hz, 푅푎푡𝑖표(푓, 푍) = 푅푎푡𝑖표(2.86 퐻푧, 푍)푒−휋훿푘(푓−2.86), (29) where  is given by equation (11). Figure 9 shows the Lg spectral ratios 푅푎푡𝑖표(푓, 푍) plotted as functions of frequency for sediment thickness ranging from zero to 10.5 km.

19

Figure 9. Lg spectral ratios 푅푎푡𝑖표(푓, 푍) from equations (15) and (16) with parameters listed in Table 4 for frequencies less than 2.86 Hz. Higher frequency values are from equations (29) and (11). At the bottom, the shaded region indicates the area bounded by the 16 percentile and 84 percentile levels for the ratio function with different sediment thickness.

Examination of Residuals The residuals are the difference between the logarithms of the observed Lg-wave Fourier amplitude spectra and the target spectra. We calculated three sets of residuals. Reference station residuals were calculated using equation (27) to define the site response. We calculated Coastal Plain residuals also using equation (27) to define the site response. We refer to the second set of residuals as the “uncorrected” Coastal Plain residuals. We calculated a third set of residuals for the Coastal Plain sites with the target spectrum defined using the Coastal Plain site response given by equation (28). We refer to this third set of residuals as the “corrected" Coastal Plain residuals. Figure 10 shows the three sets of residuals for the 8 November 2011 Oklahoma earthquake at 5 frequencies, plotted versus hypocenter distance and sediment thickness. For reference, Figure 10 also shows the mean and mean +/- one standard deviation residual values for the reference stations. The residuals for the reference stations are well behaved, with mean values near zero at all frequencies and no apparent distance dependence. In contrast, the uncorrected Coastal Plain residuals show a strong frequency dependence, with a dependence on distance and

20

Figure 10. Uncorrected and corrected Coastal Plain station residuals and reference station residuals at different frequencies plotted versus distance and Coastal Plain sediment thickness for the 08 November 2011 earthquake in central Oklahoma. sediment thickness at frequencies greater than 1 Hz. Relative to the residuals for the reference stations, the uncorrected Coastal Plain residuals tend to be positive at low frequencies (less than 21

1 Hz) and negative at higher frequencies. The corrected Coastal Plain residuals match the behavior of the reference residuals in terms of amplitude and lack of distance and sediment thickness dependence. Note that the plots of residuals versus sediment thickness show much less scatter at high frequency, compared to the residuals plotted versus distance. We consider this convincing evidence that sediment thickness plays the dominant role in explaining the variability of attenuation in the Coastal Plain. The apparent distance dependent behavior of the high- frequency uncorrected residuals in the left column of Figure 10 exists because many of the more distant stations from this earthquake lie near the Gulf coast, on extremely thick sediment (Chapman and Conn, 2016). Figures 11 and 12 show residuals for the 8 April 2011 Arkansas and 10 November 2012 Kentucky earthquakes, respectively. Although these earthquakes are widely separated in location, in both cases the patterns of the residuals are similar to those observed for the Oklahoma earthquake (Figure 10). The residuals for the reference stations are near zero at all frequencies and show no obvious distance dependence. Likewise, the uncorrected Coastal Plain residuals are mostly positive relative to the mean of the reference residuals at frequencies less than 1 Hz, whereas they are negative at higher frequencies, becoming systematically more negative as sediment thickness increases. The corrected Coastal Plain residuals match the reference residuals well, implying that our model for the ratio of the site response of the Coastal Plain to that of the reference condition (Ratio(f,Z)) in equation (28) works well for these events. The residual patterns shown in Figures 10 -12 hold for most of the earthquakes in our data set. In Figures S1-S3 of the electronic supplement to this article, we have condensed the information for all events by plotting the mean residuals for the reference stations, uncorrected Coastal Plain stations and corrected Coastal Plain stations as functions of frequency. In most cases, the mean uncorrected Coastal Plain residuals equal or exceed those of the reference stations at lower frequencies (less than 1 or at most, 5 Hz), and are less (more negative) than the mean residual of the reference stations at higher frequency. In most cases, the corrected mean residuals are closer to the values of the mean reference residuals, particularly at higher frequencies (> 1-5 Hz). Exceptions to this behavior involve the 30 November 2017 Delaware event at high frequency, the 20 November 2010 Arkansas event at low frequency, the 12 December 2018 Tennessee event at high frequency and two earthquakes that occurred in the Coastal Plain of Texas. The data sets for the Delaware, Arkansas and Tennessee events are small. The two Texas events represent important exceptional cases. They were the only two well- recorded events with epicenters within the Gulf Coastal Plain available for this study.

22

Figure 11. Same as Figure 10 but for the 08 April 2011 Arkansas earthquake.

23

Figure 12. Same as Figure 10 but for the 10 November 2012 Kentucky earthquake.

Figure 13 shows the residuals for the 20 October 2011 earthquake in southern Texas. The residuals behave in similar fashion to those shown in Figures 10-12 at frequencies less than 1 Hz: the reference residuals are near zero and uncorrected Coastal Plain residuals exceed the mean value of the reference residuals. The corrected Coastal Plain residuals show good agreement 24

Figure 13. Same as Figure 10 but for the 20 October 2011 Texas earthquake. with the reference residuals at frequencies less than 1 Hz. However, the reference residuals are very significantly negative at higher frequencies, showing little difference with the uncorrected Coastal Plain residuals. All sites experience significant high frequency attenuation, regardless of where they are located, relative to the prediction of our reference site model. On the other hand, 25

the corrected Coastal Plain residuals are much closer to zero value, suggesting that the model expressed by equation (28) is at least somewhat effective in predicting the actual ground motion for sites in the Coastal Plain from shocks located within it. The negative values of the high frequency reference residuals for the two earthquakes in the Texas Coastal Plain suggest that stations outside the Coastal Plain experience substantial Lg- wave attenuation on the source end of the path. Reciprocity suggests that it should be possible to account approximately for this behavior by using the Coastal Plain site response term (equation 28) to calculate the target spectrum for the reference stations at high frequency, assuming that the earthquake focal depths are within the sedimentary section or at least not significantly below the top of the basement. The focal depth of the 20 October, 2011 event was estimated at 3 km (Table 1), and the thickness of the Coastal Plain section is approximately 5.5 km at the epicenter. The May 17, 2012 eastern Texas event had an estimated depth of 5 km and the sediment thickness at the epicenter is approximately 4 km. We believe that these induced events probably occurred at or near the top of the basement, in which case a correction based on the thickness of the sediments at the epicenter (Z) would be appropriate. Figure 14 shows the result of correcting both the Coastal Plain residuals and the reference stations residuals, for the 20 October 2011 southern Texas earthquake, at frequencies greater than 1.0 Hz. The corrected Coastal Plain residuals and the corrected reference residuals are near zero and in good agreement. We found similar results for the 5 May 2011 eastern Texas earthquake.

Figure 14. Same as the last two rows in Figure 13 except that the residuals at reference stations (open circles) have been corrected for the attenuation effects of the sediments near the earthquake source. The sediment thickness at the epicenter is 5.5 km.

Conclusions We used both coda and Lg-wave spectral ratios to study Lg-wave propagation in the Atlantic and Gulf Coastal Plain, relative to a reference site condition. The results of the study are in the form of bi-linear equations (equations 15 and 16, with coefficients listed in Tables 4,5 and 6) that relate the Lg wave Fourier amplitude spectral ratios of the Coastal Plain sites to the reference condition as functions of sediment thickness at frequencies of 0.1, 0.3, 0.56, 0.76, 1.06, 26

1.46, 2.06 and 2.86 Hz. The spectral ratios at frequencies greater than 2.86 Hz are given by equation (29), which involves our model for differential kappa () that is a function of sediment thickness (equation 11). Equation (29) and the  model can be used to account for high- frequency attenuation that occurs for receiver locations outside the Coastal Plain for shocks located within the Coastal Plain. We observed apparent near-source, high-frequency attenuation at distant stations outside the Coastal Plain from shocks in southern and eastern Texas. The reference condition is not a “rock” site, but rather is the mean site condition of many stations located outside the Atlantic and Gulf Coastal Plain. This should be kept in mind if these results are applied in site-specific ground motion prediction. We find that significant accumulations of Coastal Plain sediment amplify the low frequencies (less than approximately 1 Hz) and attenuate high frequencies (e.g., greater than approximately 3 Hz), relative to the reference condition, with thickness of the Coastal Plain sediment being the key variable controlling geographic variability of response. The frequencies at which amplification occurs and the magnitude of the attenuation are functions of Coastal Plain sediment thickness. The results of the study may be used to develop target Fourier amplitude spectra for the stochastic method of ground motion simulation. Such simulations could be used to develop engineering response spectral ratios, (Coastal Plain/reference) as functions of earthquake magnitude, hypocenter distance and sediment thickness, provided that appropriate duration models are available.

Project Data The data used in this study are available from the Incorporated Research Institutions for Seismology Data Management Center (IRIS DMC) at http://www.iris.edu/hq/ (last accessed January, 2019

Bibliography

Aki, K., and B. Chouet (1975). Origin of coda waves: Source, attenuation, and scattering effects, J. Geophys. Res. 80, 3322–3342. Anderson, J., and S. Hough (1984). A model for the shape of the Fourier amplitude spectrum of acceleration at high frequencies, Bull. Seismol. Soc. Am. 74, 1969–1993. Atkinson, G. M. (2004). Empirical attenuation of ground-motion spectral amplitudes in southeastern Canada and the northeastern United States, Bull. Seismol. Soc. Am. 94, 1079- 1095. Atkinson, G. M., and R. Mereu (1992). The shape of ground motion attenuation curves in southeastern Canada, Bull. Seismol. Soc. Am. 82, 2014-2031. Atkinson, G. M., and D. M. Boore (2006). Earthquake ground-motion prediction equations for eastern North America, Bull. Seismol. Soc. Am. 96, 2181-2205. Atkinson, Gail M., and David M. Boore (2014). The attenuation of Fourier amplitudes for rock sites in eastern North America, Bull. Seismol. Soc. Am. 104, 513-528. Boore, D. M. (1983). Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra, Bull. Seismol. Soc. Am. 73, 1865-1894. Boore, D.M., and W.B. Joyner (1991). Estimation of ground motion at deep-soil sites in eastern North America, Bull. Seism. Soc. Am., 81, 2167-2185.

27

Boore, D.M. and E.M. Thompson (2015). Revisions to some parameters used in stochastic- method simulations of ground motion, Bull. Seism. Soc. Am., 105, 1029-1041, doi:10.1785/0120140281. Borcherdt R.D. (1970). Effects of local geology on ground motion near San Francisco Bay, Bull. Seism. Soc. Am. 60, 29-61. Brune, J. (1970). Tectonic stress and the spectra of seismic shear waves from earthquakes, J. Geophys. Res. 75, 4997-5009. Brune, J. (1971). Correction, J. Geophys. Res. 76, 5002. Burger, R. W., P. G. Somerville, J. S. Barker, R. B. Herrmann, and D. V. Helmberger (1987). The effects of crustal structure on strong ground motion attenuation relations in eastern North America, Bull. Seismol. Soc. Am. 77, 420-439. Chapman, M. C., G. A. Bollinger, M. S. Sibol and D.E. Stephenson (1990). The influence of the Coastal Plain sedimentary wedge on strong ground motions from the 1886 Charleston, South Carolina, earthquake, Earthquake Spectra, 6, 617-640. Chapman, M.C., J.N. Beale, and R.D. Catchings (2008). Q for P-waves in the sediments of the Virginia Coastal Plain, Bull. Seismol. Soc. of Am., 98, 2022-2032, doi:10.1785/0120070170. Chapman, M. C., and Godbee, R. W. (2012). Modeling geometrical spreading and the relative amplitudes of vertical and horizontal high-frequency ground motions in eastern North America, Bull. Seismol. Soc. Am. 102, 1957-1975. Chapman, Martin and Ariel Conn (2016). A model for Lg propagation in the Gulf Coastal Plain of the southern United States, Bull. Seismol. Soc. Am 106., 349-363. https://doi.org/ 10.1785/0120150197 Cramer, C.H (2018). Gulf Coast regional Q boundaries from USArray data, Bull. Seismol. Soc. Am., 108, 427-449, doi: 10.1785/0120170170. Frankel, A. (2015). Decay of S-wave amplitude with distance from earthquakes in the Charlevoix, Quebec area: Effects of radiation pattern and directivity, Bull. Seismol. Soc. Am. 105, 850-857. Frankel, A., A. McGarr, J. Bicknell, J. Mori, L. Seeber, and E. Cranswick (1990). Attenuation of high-frequency shear waves in the crust: Measurements from New York state, South Africa, and southern California, J. Geophys. Res. 95, 441–17,457. Galloway, W. E. (2008). Depositional evolution of the Gulf of Mexico sedimentary basin, in Sedimentary Basins of the United States and Canada, A. Miall (Editor), Vol. 5, Sedimentary Basins of the World, Elsevier, Amsterdam, The Netherlands, 505-548. Garrity, C.P., and D.R. Soller (2009). Database of the geologic map of North America-Adapted from the map by J.C. Reed, Jr. and others (2005), U.S. Geological Survey Data Series 424, http://pubs.usgs.gov/ds/424/ (last accessed February 2019). Gupta I.N., K.L. McLaughlin, R.A. Wagner, R.S. Jih and T.W. McElfresh (1989). Seismic wave attenuation in eastern North America, EPRI Rept. NP-6304, Electric Power Research Institute, Palo Alto, California, 171 pp. Hanks, T.C. and R.K. McGuire (1981). The character of high-frequency strong ground motion, Bull. Seismol. Soc. Am., 71, 2071-2095. Hashash, Youssef M. A., Albert R. Kottke, Jonathan P. Stewart, Kenneth W. Campbell, Byungmin Kin, Cheryl Moss, Sissy Nikolaou, Ellen M. Rathje and Walter J. Silva (2014). Reference rock site condition for Central and Eastern North America, Bull. Seismol. Soc. Am. 104, 684-701.

28

Herrick, S.M. and R.C. Vorhis (1963). Subsurface Geology of the Georgia Coastal Plain, Georgia State Division of Conservation, Dept. of Mines, Mining and Geology, Information Circular 25, 80 p. Herrmann, R. B., and A. Kijko (1983). Modeling some empirical Lg relations, Bull. Seismol. Soc. Am. 73, 157-171. Hunter, J. D. (2007). Matplotlib: A 2D graphics environment, Computing in Science & Engineering, 9(3), 90–95. Joyner, W.B., R.E. Warrick and T.E. Fumal (1981). The effect of Quaternary alluvium on strong ground motion in the Coyote Lake, California earthquake of 1979, Bull. Seism. Soc. Am. 71, 1333-1349. Kennett, B. L. N. (1986). Lg waves and structural boundaries, Bull. Seismol. Soc. Am. 76, 1133- 1141. Lawrence, D.P. and C.W. Hoffman (1993). Geology of Basement Rocks Beneath the North Carolina Coastal Plain, North Carolina Geological Survey, Division of Land Resources, Department of Environment, Health and Natural Resources, Bulletin 95, 60 p. Ou, G.-B., and R. B. Herrmann (1990). A statistical model for ground motion produced by earthquakes at local and regional distances, Bull. Seismol. Soc. Am. 80, 1397-1417. Parker, E.H., R.B. Hawman, K.M. Fischer and L.S. Wagner, (2013). Crustal evolution across the southern Appalachians: Initial results from the SESAME broadband array, Geophysical Research Letters, 40, 3853-3857 doi: 10.1002/grl.50761. Pasyanos, M.E. (2013). A lithospheric attenuation model for North America, Bull. Seismol. Soc. Am. 103, 3321-3333. PEER (2015). NGA-East: Median Ground-motion Models for the Central and Eastern North America Region, PEER Report No. 2015/04, Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA. PEER (2017). NGA-East: NGA-East Ground-Motion Models for the U.S. Geological Survey National Seismic Hazard Maps, PEER Report No. 2017/03, Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA. Powars, D.S., L.E. Edwards, S.M. Kidwell and J.S. Schindler (2015). Cenozoic stratigrahy and structure of the Chesapeake Bay region, in Tripping from the Fall Line: Field Excursions for the GSA Annual Meeting, Baltimore, 2015, D.K. Brezinski, J.P. Halka and R. A. Ortt Jr. (Editors), Geological Society of America Field Guide, Vol. 40, 171-229, doi: 10.1130/2015.0040(07). Pratt, T. L., J.W. Horton, Jr., J. Munoz, J., S.E. Hough, M.C. Chapman and C. G. Olgun (2017). Amplification of earthquake ground motions in Washington, DC, and implications for hazard assessments in central and eastern North America, Geophys. Res. Letters 44, 12,150-12,160. http://doi.org/10.1002/2017GL075517. Salvador, A. (1991a). The Gulf of Mexico Basin, Chapter 1 Introduction, in The Gulf of Mexico Basin, A. Salvadore (Editor), Vol. J, The Geology of North America, Geological Society of America, Boulder, Colorado, 1-12. Salvador, A. (1991b).Structure at the base and subcrop below Mesozoic marine section, Gulf of Mexico basin, in The Gulf of Mexico Basin, A. Salvadore (Editor), Vol. J, Plate 3,The Geology of North America, Geological Society of America, Boulder, Colorado, 1-12 Sawyer, D.S., R. T. Buffler, and A. Pilger Jr. (1991). The crust under the Gulf of Mexico basin, in The Gulf of Mexico Basin, A. Salvadore (Editor), Vol. J, The Geology of North America, Geological Society of America, Boulder, Colorado, 53-72.

29

Thomas, W. A. (2010). Interactions between the southern Appalachian-Ouachita orogenic belt and basement faults in the orogenic footwall and foreland, Geol. Soc. Am., Memoir, Vol.

Van Avendonk, J.A. Harm, Gail L. Christeson, Ian O. Norton, and Drew R.Eddy (2015). Continental rifting and sediment infill in the northwestern Gulf of Mexico, Geology 43, 631-634. Wang, C. Y., and Herrmann, R. B. (1980). A numerical study of P-, SV- and SH-wave generation in a plane layered medium, Bull. Seismol. Soc. Am. 70, 1015-1036. Wait, R.L. and M.E. Davis (1986). Configuration and Hydrology of the Pre-Cretaceous Rocks Underlying the Southeastern Coastal Plain Aquifer System, U.S. Geological Survey, Water- Resources Investigations Report 86-4010, doi:10.3133/wri864010. Wessel, P., and W. Smith (1991). Free software helps display data, Eos Trans. AGU 72, 445– 446. Wu, Q., M. C. Chapman, J. N. Beale, and S. Shamsalsadati (2016). Near-source geometrical spreading in the central Virginia seismic zone determined from the aftershocks of the 2011 Mineral, Virginia, earthquake, Bull. Seismol. Soc. Am. 106, 943–955. Wu, Qimin, and Chapman, Martin (2017). Stress-drop estimates and Source Scaling of the 2011 Mineral, Virginia, mainshock and aftershocks, Bull. Seismol. Soc. Am. 107, 2703-2720.

Author Affiliations and Address

4044 Derring Hall Department of Geosciences Virginia Tech Blacksburg, Virginia 24061 Zhen Guo: [email protected] Martin Chapman: [email protected]

Tables Table 1 Earthquakes Used in This Study

Event number State Date (dd/mm/yyyy) Latitude (°) Longitude (°) Moment Magnitude Focal Depth (km) 01 Arkansas 08/04/2011 35.261 -92.362 3.86 4 02 Arkansas 20/11/2010 35.316 -92.317 3.87 5 03 Arkansas 18/02/2011 35.271 -92.377 4.07 8 04 South Carolina 15/02/2014 33.813 -82.063 4.11 5 05 Kentucky 10/11/2012 37.135 -82.978 4.16 14 06 Delaware 30/11/2017 39.205 -75.421 4.18 3 07 Oklahoma 13/10/2010 35.202 -97.309 4.33 14 08 Tennessee 12/12/2018 35.61 -84.74 4.35 4 09 Texas 11/09/2011 32.874 -100.804 4.41 5 10 Texas 20/10/2011 28.806 -98.147 4.59 3 11 Arkansas 28/02/2011 35.265 -92.34 4.65 4 30

12 Oklahoma 05/11/2011 35.57 -96.703 4.7 3 13 Texas 17/05/2012 31.902 -94.332 4.81 5 14 Oklahoma 08/11/2011 35.541 -96.754 4.83 8 15 Oklahoma 03/09/2016 36.429 -96.923 5.55 8 16 Virginia 23/08/2011 37.936 -77.933 5.65 6 17 Oklahoma 06/11/2011 35.537 -96.747 5.65 6

Table 2 Network Instruments Used in This Study Network Instrument type Sample rate (sample/s) Number of stations TA Broadband 40 429 US Broadband 40 13 N4 Broadband 40, 100 35 Z9 Broadband 50 55 LD Broadband-short period 40, 50, 100 6

Table 3 Number of Recordings for Each Earthquake Used in This Study

Total number of Number of Coastal Plain Event number recordings recordings Distance range (km) 01 205 101 64 ~ 988 02 143 54 199 ~ 996 03 111 27 64 ~ 816 04 131 69 67 ~ 1000 05 157 92 218 ~ 996 06 41 8 170 ~ 986 07 156 56 39 ~ 898 08 97 26 68 ~ 991 09 127 77 112 ~ 897 10 67 45 33 ~ 893 11 167 71 66 ~ 900 12 217 111 24 ~ 998 13 138 68 34 ~ 997 14 193 99 25 ~ 900 15 35 13 116 ~ 964 16 25 17 434 ~ 893 17 220 109 26 ~ 984

31

Table 4

Thickness range (푍) (km) 0 < Z ≤ Z0 Z > Z0

Center frequency (Hz) Z0 (km) a1 b1 a2 b2 Error in a2 Error in b2 S.E. of estimate 𝜎 0.1 2.5 0.0 0.2449 0.4585 0.0615 0.0749 0.0092 0.6166 0.3 0.8 0.0 1.0059 0.7935 0.0140 0.0400 0.0062 0.6361 0.56 0.35 0.0 2.4482 0.8624 -0.0158 0.0381 0.0062 0.7057 0.76 0.2 0.0 3.4803 0.7077 -0.0584 0.0373 0.0063 0.7498 1.06 0.13 0.0 3.2598 0.4348 -0.0844 0.0386 0.0066 0.7970 1.46 0.07 0.0 4.1536 0.2992 -0.1202 0.0401 0.0070 0.8372 2.06 0.06 0.0 3.7848 0.2362 -0.1520 0.0423 0.0075 0.8796 2.86 0.06 0.0 1.5930 0.1056 -0.1662 0.0458 0.0083 0.9417

Table 5

Thickness range (푍) (km) 0 < Z ≤ Z0 Z > Z0

Center frequency (Hz) Z0 (km) a1 b1 a2 b2 0.1 2.5 0.0 0.4916 1.0751 0.0615 0.3 0.8 0.0 1.8011 1.4297 0.014 0.56 0.35 0.0 4.4646 1.5681 -0.0158 0.76 0.2 0.0 7.2294 1.4576 -0.0584 1.06 0.13 0.0 9.3909 1.2318 -0.0844 1.46 0.07 0.0 16.1138 1.1364 -0.1202 2.06 0.06 0.0 18.444 1.1158 -0.152 2.86 0.06 0.0 17.2875 1.0472 -0.1662

Table 6

Thickness range (푍) (km) 0 < Z ≤ Z0 Z > Z0

Center frequency (Hz) Z0 (km) a1 b1 a2 b2 0.1 2.5 0.0 -0.0017 -0.1581 0.0615 0.3 0.8 0.0 0.2107 0.1574 0.014 0.56 0.35 0.0 0.4317 0.1566 -0.0158 0.76 0.2 0.0 -0.2688 -0.0421 -0.0584 1.06 0.13 0.0 -2.8713 -0.3623 -0.0844 1.46 0.07 0.0 -7.8067 -0.5381 -0.1202 2.06 0.06 0.0 -10.8744 -0.6433 -0.152 2.86 0.06 0.0 -14.1015 -0.8361 -0.1662

32

33